Nate the Skate was an avid physics student whose main non-physics interest in li

Question

Nate the Skate was an avid physics student whose main non-physics interest in life was high-speed skateboarding. In particular, Nate would often don a protective suit of Bounce-Tex, which he invented, and after working up a high speed on his skateboard, would collide with some object. In this way, he got a gut feel for the physical properties of collisions and succeeded in combining his two passions. On one occasion, the Skate, with a mass of 129 kg, including his armor, hurled himself against a 877-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.63 m/s and Nate bounced backward. What were Nate's speeds immediately before and after the collision? (Enter positive numbers.) Ignore friction with the ground. 'By the way, this brief bio of Nate the Skate is written in the past tense, because not long ago he forgot to put on his Bounce-Tex before colliding with the Washington Monument in a perfectly inelastic collision. We will miss him.

Explanation / Answer

M×U + M×U = M×V + M×V
and
U - U = V - V
where
M = mass 1 = 129 kg
M = mass 2 = 877kg
U = speed of mass 1 before collision = ?
U = speed of mass 2 before collision = 0 m/s
V = speed of mass 1 after collision = ?
V = speed of mass 2 before collision = 1.63 m/s
so
129×U + 877×0 = 129×V + 877×1.63
129×U =129×V + 1429.51 . . . . . . . .(equation 1)
and
U - 0 = 1.63 - V
U = 1.63 - V . . . . . . . . . . . . . . . . . . (equation 2)

substitute (equation 2) in (equation 1)

129×(1.63 - V) = 129×V + 1429.51
210.27 -129×V = 129×V + 1429.51
-1219.24 = 258×V
V = - 4.72 m/s

substitute that value in (equation 2)

U = 1.63 - (- 4.72)
U = 6.35 m/s

Answer:
Nate's speed immediately before the collision is 6.35 m/s (forwards)
Nate's speed immediately after the collision is 4.72 m/s (backwards)

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